Question: Simplify the following expression: $n = \dfrac{-10p^2 + 30p - 20}{p - 2} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ n =\dfrac{-10(p^2 - 3p + 2)}{p - 2} $ Then we factor the remaining polynomial: $p^2 {-3}p + {2} $ ${-2} {-1} = {-3}$ ${-2} \times {-1} = {2}$ $ (p {-2}) (p {-1}) $ This gives us a factored expression: $\dfrac{-10(p {-2}) (p {-1})}{p - 2}$ We can divide the numerator and denominator by $(p + 2)$ on condition that $p \neq 2$ Therefore $n = -10(p - 1); p \neq 2$